In another direction, an interesting class of Poisson manifolds closely related to Poisson-Lie groups are Poisson homogeneous spaces, given by the quotient \(G/H\)  of a Poisson-Lie group \(G\)  with a closed Lie subgroup \(H\)  of \(G\)  (see [1]}). As an extension of the results in this paper, it would be interesting to discuss the existence of invariant volume forms for Hamiltonian systems on \(G/H\) . In this setting we remark the following facts:
